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Zig-zag and replacement product graphs and LDPC codes
1. | Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, United States |
2. | 1251 Waterfront Place, Seagate Technology, Pittsburgh, PA 15222, United States |
3. | Institut für Mathematik, Universität Zürich, Zürich, CH-8057 |
[1] |
Srimathy Srinivasan, Andrew Thangaraj. Codes on planar Tanner graphs. Advances in Mathematics of Communications, 2012, 6 (2) : 131-163. doi: 10.3934/amc.2012.6.131 |
[2] |
Dina Ghinelli, Jennifer D. Key. Codes from incidence matrices and line graphs of Paley graphs. Advances in Mathematics of Communications, 2011, 5 (1) : 93-108. doi: 10.3934/amc.2011.5.93 |
[3] |
Sara D. Cardell, Joan-Josep Climent. An approach to the performance of SPC product codes on the erasure channel. Advances in Mathematics of Communications, 2016, 10 (1) : 11-28. doi: 10.3934/amc.2016.10.11 |
[4] |
Fernando Hernando, Diego Ruano. New linear codes from matrix-product codes with polynomial units. Advances in Mathematics of Communications, 2010, 4 (3) : 363-367. doi: 10.3934/amc.2010.4.363 |
[5] |
Christine A. Kelley, Deepak Sridhara. Eigenvalue bounds on the pseudocodeword weight of expander codes. Advances in Mathematics of Communications, 2007, 1 (3) : 287-306. doi: 10.3934/amc.2007.1.287 |
[6] |
Fernando Hernando, Tom Høholdt, Diego Ruano. List decoding of matrix-product codes from nested codes: An application to quasi-cyclic codes. Advances in Mathematics of Communications, 2012, 6 (3) : 259-272. doi: 10.3934/amc.2012.6.259 |
[7] |
Shuangliang Tian, Ping Chen, Yabin Shao, Qian Wang. Adjacent vertex distinguishing edge-colorings and total-colorings of the Cartesian product of graphs. Numerical Algebra, Control and Optimization, 2014, 4 (1) : 49-58. doi: 10.3934/naco.2014.4.49 |
[8] |
Jennifer D. Key, Washiela Fish, Eric Mwambene. Codes from the incidence matrices and line graphs of Hamming graphs $H^k(n,2)$ for $k \geq 2$. Advances in Mathematics of Communications, 2011, 5 (2) : 373-394. doi: 10.3934/amc.2011.5.373 |
[9] |
Cristóbal Camarero, Carmen Martínez, Ramón Beivide. Identifying codes of degree 4 Cayley graphs over Abelian groups. Advances in Mathematics of Communications, 2015, 9 (2) : 129-148. doi: 10.3934/amc.2015.9.129 |
[10] |
Ricardo A. Podestá, Denis E. Videla. The weight distribution of irreducible cyclic codes associated with decomposable generalized Paley graphs. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021002 |
[11] |
Joaquim Borges, Josep Rifà, Victor A. Zinoviev. Families of nested completely regular codes and distance-regular graphs. Advances in Mathematics of Communications, 2015, 9 (2) : 233-246. doi: 10.3934/amc.2015.9.233 |
[12] |
Emmanuel Charbit, Irène Charon, Gérard Cohen, Olivier Hudry, Antoine Lobstein. Discriminating codes in bipartite graphs: bounds, extremal cardinalities, complexity. Advances in Mathematics of Communications, 2008, 2 (4) : 403-420. doi: 10.3934/amc.2008.2.403 |
[13] |
Washiela Fish, Jennifer D. Key, Eric Mwambene. Binary codes from reflexive uniform subset graphs on $3$-sets. Advances in Mathematics of Communications, 2015, 9 (2) : 211-232. doi: 10.3934/amc.2015.9.211 |
[14] |
Hans-Joachim Kroll, Sayed-Ghahreman Taherian, Rita Vincenti. Optimal antiblocking systems of information sets for the binary codes related to triangular graphs. Advances in Mathematics of Communications, 2022, 16 (1) : 169-183. doi: 10.3934/amc.2020107 |
[15] |
Peter Vandendriessche. LDPC codes associated with linear representations of geometries. Advances in Mathematics of Communications, 2010, 4 (3) : 405-417. doi: 10.3934/amc.2010.4.405 |
[16] |
Padmapani Seneviratne, Martianus Frederic Ezerman. New quantum codes from metacirculant graphs via self-dual additive $\mathbb{F}_4$-codes. Advances in Mathematics of Communications, 2022 doi: 10.3934/amc.2021073 |
[17] |
Dean Crnković, Marija Maksimović, Bernardo Gabriel Rodrigues, Sanja Rukavina. Self-orthogonal codes from the strongly regular graphs on up to 40 vertices. Advances in Mathematics of Communications, 2016, 10 (3) : 555-582. doi: 10.3934/amc.2016026 |
[18] |
Ken Saito. Self-dual additive $ \mathbb{F}_4 $-codes of lengths up to 40 represented by circulant graphs. Advances in Mathematics of Communications, 2019, 13 (2) : 213-220. doi: 10.3934/amc.2019014 |
[19] |
Bernardo Gabriel Rodrigues. Some optimal codes related to graphs invariant under the alternating group $A_8$. Advances in Mathematics of Communications, 2011, 5 (2) : 339-350. doi: 10.3934/amc.2011.5.339 |
[20] |
Dean Crnković, Ronan Egan, Andrea Švob. Self-orthogonal codes from orbit matrices of Seidel and Laplacian matrices of strongly regular graphs. Advances in Mathematics of Communications, 2020, 14 (4) : 591-602. doi: 10.3934/amc.2020032 |
2020 Impact Factor: 0.935
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